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A massless inextensible string in the form of a loop is placed on a horizontal film of soap solution of surface tension T. If film is pierced inside the loop and it convert into a circular loop of diameter d, then the tension produced in string is- 1) Td, 2) πTd, 3) πd^2T, 4) πd^2T/4

Asked by patra04011965 12th January 2019, 1:20 PM
Answered by Expert

Figure shows a length Δl of loop subjected to Tension F and surface tension forces.
Tension force F is acting tangentially and can be resolved into horizontal components F cos(θ/2) and vertical components F sin(θ/2).
where θ is the angle subtended by Δl at center.
Horizontal components cancel each other.  Vertical components of tension is balanced by surface tension force 2TΔl.
2F sin(θ/2) = 2TΔl = 2T×rθ
r is radius and let d be diameter of loop
Hence F = T×rθ/ sin(θ/2)  = 2r×T = d×T  [ we have assumed for small angle sin(θ/2) = θ/2 ]
Answered by Expert 13th January 2019, 12:00 AM
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